Question

Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are 

-2, 1, -1 and -3, -4, 1

Answer 1

Let a, b, c be the direction ratios of the vector which is perpendicular to the two lines whose direction ratios are -2, 1, -1 and -3, -4, 1

∴ -2a + b – c = 0 and -3a – 4b + c = 0

∴ the required direction ratios are -3, 5, 11 

Alternative Method:

Let \(\overline{a}\) and \(\overline{b}\) be the vectors along the lines whose direction ratios are -2, 1, -1 and -3, -4, 1 respectively.

The vector perpendicular to both \(\overline{a}\) and \(\overline{b}\) is given by

Hence, the required direction ratios are -3, 5, 11.